"Is memorization a good strategy for learning mathematics?"
April 23, 2016
I just read an interesting article from the OECD web page.
The article is analyzing research data from PISA tests and finds a really reasonable conclusion.
"Students who avoid making an effort to understand mathematics concepts may succeed in some school environments; but a lack of deep,critical and creative thinking may seriously penalise these students later in life when confronted with real, non-routine problems."
"In some situations, memorisation is useful, even necessary. It can give students enough concrete facts on which to reflect; it can limit anxiety by reducing mathematics to a set of simple facts, rules and procedures; and it can help to develop fluency with numbers early in a child’s development, before the child is asked to tackle more complex problems. But to perform at the very top, 15-year-olds need to learn mathematics in a more reflective, ambitious and creative way – one that involves exploring alternative ways of finding solutions, making connections,adopting different perspectives and looking for meaning. So yes, you can use your memory, just use it strategically."
In my opinion, learning mathematics is not too different than learning for example basketball. Everyone has to start with the fundamentals! In mathematics, learn numbers, operations, math terms, basic definitions, etc. In basketball, learn how to shoot, dribble, and memorize the basic plays. Without the basics, students and players have no chance to succeed in any field. Trying to do math without knowing how to add or multiply is like trying to play in NCAA without knowing how to dribble with both hands. The chance it can happen is really unlikely.
I would say memorization is important, it is the base of all knowledge. Without memory there is no knowledge. But the way, how a lot of students try to do it is not too efficient. This is from where the frustration is coming. Forcing our brain to suck up the information is not always efficient. Different people have different memories. The lucky ones have photographic memory but most of us have to repeat information again and again to store it in the long term memory. The key is continuous repetition. More frequently at the beginning, and less and less when the information becomes recallable any time without a problem. Exactly like in sports. Brain memory is like muscle memory. You can imagine how to dribble and try to remember how you did it two weeks ago, but if you really want to be better, you have to practice it every day ! Trying to do math just relying on the teacher explanation without practice won't work. Pupils have to practice the new skills ! Just watching the NBA won't make anyone an NBA player. Just watching YouTube videos about math can help to understand the concept, but without actual practice students won't be better in math.
So memorization with practice definitely helps at the beginning, just find your own method.
Later, when the foundations are solid, memorization won't help as much because math becomes much more complex. Intuition becomes more and more important as students start to see math as a whole not just parts.
There are no particular formulas that could solve every problem. Starting from high school, the problems become more challenging and they require strategies, logic and experience to get to the solution. In college, problems become abstract and more difficult to understand without strong foundations. Memorization becomes less important. At this time, most people who have been studying mathematics consistently from elementary school already have developed strong and reliable understanding based knowledge, but students who tried to take the short path of learning will pay the price.